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      Refined global Gross-Prasad conjecture on special Bessel periods and B\"ocherer's conjecture

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          Abstract

          In this paper we pursue the refined global Gross-Prasad conjecture for Bessel periods formulated by Yifeng Liu in the case of special Bessel periods for SO(2n+1)×SO(2). Recall that a Bessel period for SO(2n+1)×SO(2) is called special when the representation of SO(2) is trivial. Let π be an irreducible cuspidal tempered automorphic representation of a special orthogonal group of an odd dimensional quadratic space over a totally real number field F whose local component πv at any archimedean place v of F is a discrete series representation. Let E be a quadratic extension of F and suppose that the special Bessel period corresponding to E does not vanish identically on π. Then we prove the Ichino-Ikeda type explicit formula conjectured by Liu for the central value L(1/2,π)L(1/2,π×χE), where χE denotes the quadratic character corresponding to E. Our result yields a proof of B\"ocherer's conjecture on holomorphic Siegel cusp forms of degree two which are Hecke eigenforms.

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          On Whittaker vectors and representation theory

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            Transcending classical invariant theory

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              On the Periods of Automorphic Forms on Special Orthogonal Groups and the Gross–Prasad Conjecture

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                Author and article information

                Journal
                2016-11-17
                Article
                1611.05567
                496b08c5-9687-4041-ab2f-a424b8bcb693

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Primary: 11F55, 11F67, Secondary 11F27, 11F46
                25 pages
                math.NT math.RT

                Number theory,Algebra
                Number theory, Algebra

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